Welcome aboard Tweed! And congratulations on your decision to buy a Corvette! You wont regret it!
As for tips on what to buy and what not to buy, I personaly dont like buying a car from the first year of a new generation. It maybe superstision, but it seems that the first year of a new generation has the most problems cause they are getting the kinks out of the system. This applys to all cars not just Corvettes.
As to Corvettes, I dont know what your price range is, I would recomend a '79-'82 Shark. They can be had anywhere from 8k up to 20k and maybe a little more. The cheaper ones will have issues, like high miles, or poor maintence, but can make great project cars. A word of warning though, they are pretty under powered by todays standards. A L82 engine is rated at 220hp, and the L48 engine is rated at 180?hp. If you want something a little more powerfull you can move up into the C4 era. '90-'92 ZR-1's can be had for under 30k. That will buy you your own 370hp LT-5 powered "King of the Hill" The '93-'95 ZR-1 are a little more expensive, I have seen them ranging up into the 50k area. Or you can go for my personal favorate: a '96 with an LT-4 powerplant. Conservitivly rated at 330hp (acctualy closer to 345) you will have more than enough power to hold even with (and probably pass) a C5 with light modds. The LT-4 was only avalible in '96 but it was in three diffrient Corvettes, the Grand Sport (for which the engine was built) of which only 1,000 where made. If you are luck enough to see one for sale they usualy go for about 30K, but can vary a lot depending on the cars history, miles and modds. Chevy also put the LT-4 in the Collectors Edition Corvette. These cars are painted silver and have aliuminum GS wheels. Chevy built about 5,000 of these and as such they are a little bit cheaper than the GS's. And finaly, all the remaining Corvettes produced that year with the ZF-6 tranny came with the LT-4.
I hope this helps in your decision.